On a Problem Posed by Luigi Campedelli
Stagnaro, Ezio
Bollettino dell'Unione Matematica Italiana, Tome 4 (2011), p. 237-243 / Harvested from Biblioteca Digitale Italiana di Matematica
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We construct an irreducible degree 10 plane curve C10, giving the explicit equation with real coefficients, having six [3; 3] points that are not on a conic. The fairly simple equation of C10 enables the shape of a curve, whose equation has been researched without success since 1932, to be visualized in the real plane.

Publié le : 2011-06-01
@article{BUMI_2011_9_4_2_237_0,
     author = {Ezio Stagnaro},
     title = {On a Problem Posed by Luigi Campedelli},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4},
     year = {2011},
     pages = {237-243},
     zbl = {1230.14042},
     mrnumber = {2840604},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_2_237_0}
}

Stagnaro, Ezio. On a Problem Posed by Luigi Campedelli. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 237-243. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_2_237_0/

[C1] Campedelli, L., Sui piani doppi con curva di diramazione del decimo ordine, Atti. Acc. Naz. Lincei, Rendiconti, Vol. XV (1932), 358-362.

[C2] Campedelli, L., Sopra alcuni piani doppi notevoli con curva di diramazione del decimo ordine, Atti. Acc. Naz. Lincei, Rendiconti, Vol. XV (1932), 536-542.

[D] Dolgachev, I., Algebraic surfaces with q=py=0, Algebraic Surfaces, C.I.M.E., Cortona-Varenna 1977, Liguori ed., Napoli (1981), 97-215. | MR 2757651

[R] Reid, M., Campedelli versus Godeaux, in ``Problems in the theory of surfaces and their classification'', (Cortona, 1988), Academic Press (1991), 309-365. | MR 1273384

[S1] Stagnaro, E., On Campedelli branch loci, Annali Univ. Ferrara - Sez. VII - Sc. Mat., Vol. XLIII (1997), 1-26. | MR 1686746

[S2] Stagnaro, E., What decides the existence of a branch curve? (A new Campedelli branch curve C1+C9), to appear on ``Atti Acc. Ligure di Sc. e Lett.''. | MR 2808000

[W] Werner, C., Branch curves for Campedelli double planes, Rocky Mt. J. Math.36, No. 6 (2006). 2057-2073. | MR 2305646 | Zbl 1143.14033